How do I graph x<2y and x+y<0
To graph the inequalities x < 2y and x + y < 0, we can follow these steps:
Step 1: Graph the equation x = 2y
- This equation represents a straight line with a slope of 1/2 passing through the origin (0,0). Choose a few points on the line, such as (-2,-1), (0,0), and (2,1), and draw the line connecting them.
Step 2: Shade the region below the line x = 2y
- Since the inequality is x < 2y, we want to shade the region below the line x = 2y. This represents all the points where x is less than 2 times y.
Step 3: Graph the equation x + y = 0
- This equation represents a straight line with a slope of -1 passing through the origin (0,0). Choose a few points on the line, such as (-1,1), (0,0), and (1,-1), and draw the line connecting them.
Step 4: Shade the region below the line x + y = 0
- Since the inequality is x + y < 0, we want to shade the region below the line x + y = 0. This represents all the points where the sum of x and y is less than zero.
Step 5: Identify the region where both conditions are true
- The solution to the system of inequalities is the region where both shaded areas overlap. This represents the set of points that satisfy both x < 2y and x + y < 0.
Here is a visual representation of the graph:
/|
/ |
____/__|____
/ | x < 2y
/______|
\________
\ |
x + y < 0
The shaded area below the line x = 2y and below the line x + y = 0 is the region that satisfies both inequalities.